Math 8 Unit 6 Notes Name: _____________

6.1 – Solving Equations using Models (pp. 318-326)

There are a couple of different models we can use to help solve simple equations.

1) Using balance scales

2) Using algebra tiles

Ex. 3 Three more than six times a number is 21. Let n represent the number.

a) Write an equation you can use to solve for n.

b) Represent the equation with tiles. Use the tiles to solve the equation. Sketch the tiles you used.

6.2 – Solving Equations using Algebra (pp. 327-332)

To solve an equation, we need to isolate the variable on one side of the equation. To do this, we get rid

of the numbers on that side of the equation.

When we solve an equation using algebra, we must also preserve the equality. Whatever we do to one

side of the equation, we must do to the other side, too.

Ex. 1

a) Solve using algebra : 16t – 69 = 13

b) Verify the solution

Ex. 2 Use algebra to solve each equation. Verify the solution.

a) 4x =16

b) 12 =3x

c) 21 = 7x

d) 6x = 30

Ex. 3 Navid now has $72 in her savings account. Each week she will save $24. After how many weeks

will Navid have a total savings of $288?

a) Write an equation you can use to solve the problem.

b) Solve the equation. When will Navid have $288 in her savings account?

c) Verify the solution.

Ex. 4 The Grade 8 students had an end-of-the-year dance. The disc jockey charged $85 for setting up

the equipment, plus $2 for each student who attended the dance. The disc jockey was paid $197.

How many students attended the dance?

a) Write an equation you can use to solve the problem.

b) Solve the equation.

c) Check your answer and explain how you know it is correct

6.3 – Solving Equations involving Fractions (pp. 333-337)

Ex. 2 One-quarter of the golf balls in the bag are yellow. There are 8 yellow golf balls. How many golf

balls are in the bag?

a) Write an equation you can use to solve the problem.

b) Solve the equation.

c) Verify the solution.

Ex. 3 Solve each equation.

Ex. 4 For each sentence, write an equation. Solve the equation to find the number.

a) Add 1 to a number divided by -3 and the sum is 6.

b) Subtract a number divided by 9 from 3 and the difference is 0.

c) Add 4 to a number divided by -2 and the sum is -3.

Ex.5 One-third of the Grade 8 students went to the track-and-field meet. Five track coaches went too.

There were 41 people on the bus, not including the driver. How many students are in Grade 8?

a) Write an equation you can use to solve the problem.

b) Solve the equation.

c) Verify the solution

6.4 – The Distributive Property (pp. 338-343)

distributive property: the property stating that a product can be written as a sum or difference of two

products; for example,a(b+ c) = ab+ ac, a(b– c) = ab– ac

Ex. 4 Write two formulas for the perimeter, P, of a rectangle. Explain how the formulas illustrate the

distributive property.

Ex. 5 There are 15 players on the Grade 8 baseball team. Each player needs a baseball cap and a team

jersey. A team jersey costs $25. A baseball cap costs $14.

a) Write 2 different expressions to find the cost of supplying the team with caps and jerseys.

b) Evaluate each expression. Which expression did you find easier to evaluate? Explain

Ex. 6 Five friends go to the movies. They each pay $9 to get in, and $8 for a popcorn and drink combo.

a) Write 2 different expressions to find the total cost of the outing.

b) Evaluate each expression. Which expression was easier to evaluate? Justify your choice

6.5 – Solving Equations Involving the Distributive Property (pp.

344-348)

Ex. 2 Solve each equation using the distributive property.

Verify the solution.

a) 3(x +5) =36

b) 4(p-6) =36

c) 5(y+2) =25

d) 10(a+8) =30

Ex. 3 The price of a souvenir T-shirt was reduced by $5. Jason bought 6 T-shirts for his friends.

The total cost of the T-shirts, before taxes, was $90. What was the price of a T-shirt before it was

reduced?

a) Write an equation to model this problem.

b) Solve the equation.

Ex. 4 Mario chose an integer. He subtracted 7, then multiplied the difference by –4. The product was

36. Which integer did Mario choose?

a) Write an equation you can use to solve the problem.

b) Solve the equation.

Ex. 5 Amanda’s office has 40 employees. The employees want to have a catered dinner. They have

found a company that will provide what they need for $25 per person. Amanda knows that some

people will bring a guest. The company has budgeted $1500 for this event. How many guests can they

invite? Assume the price of $25 includes all taxes.

a) Write an equation for this problem.

b) Solve the equation.

c) Verify the solution.

6.6 – Creating a Table of Values (pp. 351-358)

Linear relation: a relation that has a straight-line graph

Ordered pair: two numbers in order, for example, (2, 4); on a coordinate grid, the first number is the

horizontal coordinate of a point, and the second number is the vertical coordinate of the point

Ex. 2 Copy and complete the following tables of values:

Ex. 3 The equation of a linear relation is: y–2x + 7

Find the missing number in each

ordered pair.

a) (–8,____ )

b )(12,____ )

c) (____ , 31)

d) (____ , –23)

6.7 – Graphing Linear Relations (pp. 359-365)

Ex. 2 Peter’s Promoting is organizing a concert. The cost of the venue and the rock band is $15 000.

Each concert ticket sells for $300. Peter’s profit is the money he makes from selling tickets minus the

cost. Let n represent the number of tickets sold. Let p represent Peter’s profit. An equation that

relates the profit to the number of tickets sold is: p= 300n-15 000

a) Create a table of values for the relation. Use these values of n: 10, 20, 30, 40, 50, 60, 70, 80

b) Graph the relation. What do negative values of p represent?

c) Describe the relationship between the variables in the graph.

d) How can you use the graph to find the profit when 75 tickets are sold?